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)R/ffORY 

iiANUAL 

IN 

PHYSICS 



WAUCHOPE 




Gopgtafi?. 



COKTRIGliT DEPOSIT 



LABORATORY MANUAL 



IN 



PHYSICS 



BY 

JOSEPH A. WAUCHOPE 

THE MECHANICS ABTS HIGH SCHOOL ST. PAUL 



SCOTT, FORESMAN AND COMPANY 
CHICAGO NEW YORK 






COPYRIGHT 1912 
By SCOTT. FORESMAN AND COMPANY 



CCIA319750 



PREFACE 

This manual has been prepared to meet the modern 
demand on the part of high school instructors of 
Physics for a set of experiments which will connect the 
laboratory work more closely with the everyday 
experiences of the student. 

To send the pupil into the laboratory to " Determine 
the Magnitude and Point of Application of the Result- 
ant of Two Parallel Forces Acting in the Same 
Direction," ''Determine the Coefficient of Linear Ex- 
pansion of a Metallic Rod," or "Find the Focal Length 
of a Convex Lens," is to give him a task in which 
he has very little interest. Laboratory exercises 
should be motivating. They should be based on 
problems which arise naturally from daily observations 
and which can only be solved by laboratory experi- 
ments. Moreover, the natural method of reasoning 
employed by the student of high school age is from 
the particular to the general. It is better, then, to 
use the laboratory to solve such problems as finding 
where a load should be placed on a pole between a 
man and a boy so that each will carry his share, or 
the amount of expansion of a steel bridge on a hot 
summer day, or the reason for wearing convex 
glasses to correct far-sightedness. This method of 
treatment gives interest and significance to the 
work and also teaches the pupils the laws of Physics 
in a much more efficient way without requiring 
special or elaborate apparatus. 



4 Preface 

An effort has been made to eliminate "busy work" 
and to offer only those laboratory exercises which are 
really worth while as teaching principles of Physics 
and in which the student can "see some use." Addi- 
tional experiments of a practical nature, making use 
of commercial forms of apparatus, thoroughly provide 
for a full year's work. 

The questions and problems introduced in the 
"Discussion" under each experiment constitute an 
important feature so often neglected in connection 
with laboratory work, and serve to illuminate the 
meaning and widen the range of association of the 
principles involved. Many more questions of a like 
nature will suggest themselves to the student and 
teacher. This discussion should follow the experi- 
ment immediately and not be delayed until it can be 
taken up in the class room. 

The manual is arranged by topics and experiments 
primarily to accompany Mann and Twiss' Physics, 
but can, of course, be used with any text. To facili- 
tate a wider range of selection by the instructor, a 
number of additional experiments have been outlined 
under Appendix I. 

The author wishes to express the highest appre- 
ciation of the assistance given by Dr. C. R. Mann in 
the preparation of the manual. Grateful acknowledg- 
ment is also made for helpful suggestions received 
from many high school instructors. 

J. A. WAUCHOPE. 

June 1, 1912. 



CONTENTS 

MECHANICS 

The Inclined Plane 7 

The Pulley 9 

The Wheel and Axle 12 

The Lever 13 

Equilibrant 15 

Resultants 17 

Water Pressure 19 

Weight of Air 20 

The Hydraulic Press 21 

Boyle's Law 23 

Comparative Densities 25 

Specific Gravity 26 

Archimedes Principle 27 

Efficiency of Water Motors 28 

HEAT 

Good and Poor Conductors 32 

Temperature of Boiling Water 33 

Coefficient of Linear Expansion 35 

Heat of Vaporization of Water 37 

The Dew Point 40 

Evaporation 41 

Air Pressure and Boiling Point of Water 43 

Heat of Fusion of Ice 44 

Specific Heat 45 

Heat of Combustion 47 

Thermal Efficiency 49 

ELECTRICITY AND MAGNETISM 

Polarization 51 

Magnetic Fields 52 

Strength of Electro-Magnets 53 

5 



6 Contents 

Electrical Resistances 54 

Electromotive Force. . 57 

The Working of an Electric Motor 58 

Electro-Plating 60 

The Fall of Potential 62 

Carbon Filament Lamps 64 

Advantage of Parallel Connections 66 

Arc Lamp 67 

Efficiency of Electro-Motors 68 

Heat Produced by Electrical Power 71 

SOUND 

Cause of Different Tones 73 

Velocity of Sound , . . . 74 

Effect of Tension and Length on Number of Vibrations 76 

LIGHT 

Use of Pupil of the Eye 78 

Convex and Concave Lenses 79 

The Telescope 81 

Candlepower 82 

Efficiencies of Carbon Filament and Tungsten Lamps 84 

APPENDIX I. 

Tension and Breaking-Strength 86 

Elasticity 87 

Pendulum Vibrations 89 

Accelerated Motion 90 

The Wheatstone Bridge 93 

Voltage 95 

Images 97 

Refraction 98 

APPENDIX II. (Tables) 

Densities of Solids, Liquids, and Gases 101 

Specific Heats . 101 

Diameter of Wires 102 

Useful Data 103 



LABORATORY MANUAL IN PHYSICS 



EXPERIMENT No. 1 
PART I 

Question. — Does it require more work to slide a cake 
of ice up an inclined plane than to lift it vertically to 
the top of the plane? 

Apparatus. — Inclined plane; block of iron weighing 
several pounds; spring balance. 

Remarks. — Work is expressed in foot-pounds and is 
determined by multiplying together the number of 
pounds of force and the number of feet of distance 
through which the force acts. One foot-pound = 
1 pound X 1 foot. 




Directions. — Find the weight of the block and the 
height CB of the plane. The product of these two 
will give the work done in lifting the block vertically. 
Now find the length AB of the plane and the force 
required to draw the block with uniform speed up the 
plane as indicated by the spring balance. The prod- 



8 Laboratory Manual in Physics 

uct of these two will give the work done in drawing 
the block up the plane. Call the weight of the block 
the resistance and the force exerted along the plane 
the effort, and record your results as follows: 
Results. — 

Resistance = lb. 

Effort = lb. 

Resistance X height of plane = 

foot-pounds. 

Effort X length of plane = 

foot-pounds. 

Discussion. — The work done on this machine, that 
is, effort X length, is known as the input. The work 
performed by the machine, that is, resistance X 
height, is known as the output. Which is greater, the 
input , or the output? What causes this difference? 



PART II 

Question. — What is the efficiency of the inclined 
plane used in this experiment? Would the use of a 
smoother surface on the incline make any difference 
in the efficiency of the machine? 

Apparatus. — Same as Part I; glass plate. 

Remarks. — By the efficiency of a machine is meant 

the ratio of the work gotten out of it to the work put 

into it; or, 

Output . 

- = Efficiency 

Input 

Efficiency is expressed in per cent. 



Mechanics 9 

Directions, — Using the results obtained in Part I, 
calculate the efficiency of the inclined plane. Now 
substitute the glass plate for the wood surface. Obtain 
results as before and determine the efficiency. Record 
your results as follows: 

Results. — r. . , 

ttt. t i r T^rr > Output 

With wood surface : Efficiency = -7 7 = — = 

w Input 

With glass surface : Efficiency = - 



w Input 

Discussion. — What causes the difference in efficiency 
in the two trials made? If the block is mounted on 
rollers or placed in a small car is the efficiency of the 
plane greater? What further improvement can you 
suggest to increase the efficiency of the plane? Can 
you make a plane with an efficiency of 100%? How 
and why? This is known as an ideal inclined plane. 
How may we find the relations between input and 
output for an ideal plane? 

EXPERIMENT No. 2 

Question. — Is more work required to pull a safe up 
to the third floor with pulleys than to carry it up by 
hand? 

Apparatus. — Two pulleys, one fixed, the other mov- 
able; block of iron weighing several pounds; a pail; 
shot. 

Directions. — Arrange the apparatus as shown in the 
diagram. Pour shot slowly into pail E until just 



10 Laboratory Manual in Physics 

enough is contained to raise the block with uniform 
speed. Making use of two yardsticks, measure how 
far the pail moves downward in order to raise the block 
one foot. Find the weight of the block, also of the 
pail of shot. The work done by the pail of shot in 
raising the block one foot is found by multiplying 
together the weight of the pail of shot in pounds 



E 



A 



On 




and the distance in feet through which it moves down- 
ward, and is expressed by foot-pounds. The work 
done in raising the block by hand through one foot 
is evidently the weight of the block in pounds multi- 
plied by the distance of one foot. Call the weight of 
the block the resistance and the weight of the pail of 
shot the effort and record your results as follows: 



Mechanics 1 1 

Results. — 

Resistance = lbs. 

Effort = lbs. 

Resistance X distance it was raised = 
foot-pounds. 

Effort X distance it moved downward = 

foot-pounds. 

Discussion. — The number of foot-pounds of work 

gotten out of this machine, that is, the product of the 

resistance by the distance it was raised, is known as 

the output. The number of foot-pounds of work done 

on the machine, that is, the product of the effort by 

the distance it moved downward, is known as the 

input. Which is greater, the output or the input? 

What causes this difference? What is the efficiency 

of the above arrangement of pulleys? To determine 

this, divide the output by the input, or, 

Output . 

-j— = Efficiency 

Calculate the efficiency and express it in per cent. 
Is it necessary to measure the distances moved by the 
block and the pail in order to determine the efficiency? 
How could you improve the pulleys to make them 
more efficient? What is an ideal pulley? Of what 
use is it? Is it possible to make a real pulley with 
an efficiency of 100%? Why and how? 



12 Laboratory Manual in Physics 

EXPERIMENT No. 3 



Directions. — Repeat 

Experiment No. 2, using 
the wheel and axle device 
instead of the pulleys. 
Obtain results as in the 
preceding experiment and 
calculate the efficiency of 
the machine. 

Discussion. — Is it neces- 
sary to measure the dis- 
tances moved? Why? What 
else might we measure? 
How improve wheel and 
axle to get greater effi- 
ciency? Is the wheel and 
axle better than pulleys 
for raising water in buckets 
from a well? Why? Is a 
wheel and axle device ever 
used in moving houses? 
How? Have you ever seen 
one at work? Where? 




EXPERIMENT No. 4 

Question. — Does it require less work to lift a stone 
with a crow bar than to raise it directly by hand 
through the same height? 



Mechanics 13 

Apparatus. — Lever; iron block weighing several 
pounds; a pail; shot. 

Remarks. — Work is expressed in foot-pounds and is 
determined by multiplying together the number of 
pounds of force used and the number of feet of space 
through which the force acts. One foot-pound = 
1 pound X 1 foot. 



fi im ii mn i n ii 



Directions. — Find the weight of the block and calcu- 
late how much work it would take to raise it vertically 
by hand to a height of one-half of a foot. Now 
arrange the apparatus as shown in the diagram with 
the block suspended about a foot from the fulcrum 
and the pail near the end of the lever. Pour shot 
slowly into the pail until just enough is obtained to 
raise the block with uniform speed. Making use of 
two yardsticks, measure how far the pail moves 
downward in order to raise the block one-half of a 
foot. Weigh the pail of shot. The number of foot- 
pounds of work done by the pail of shot in raising the 
block one-half of a foot is the product of the weight 
of the pail by the distance it moved downward. Call 
the weight of the block the resistance and the weight 
of the pail of shot the effort, and record your results 
as follows: 



14 Laboratory Manual in Physics 

Results. — 

Resistance = lbs. 

Effort = lbs. 

Resistance X distance it was raised = 

foot-pounds. 

Effort X distance it was lowered = 

foot-pounds. 

Discussion. — You are now ready to answer the 
question: Does it take more work to raise a weight 
by hand or to lift it by means of a lever? 

Calculate the efficiency of the machine used in this 
experiment, following directions given under Dis- 
cussion, Experiment No. 2. Why is the efficiency of 
the lever greater than that of the inclined plane or 
pulleys used in Experiments 1 and 2? 

Do we need ro measure the distances moved 
through? Why? Can a lever be made with an 
efficiency of 100%? Why? Repeat the experiment 
with the fulcrum out of center, and note whether the 
efficiency of the lever ever seems to be greater than 1 ? 
Is it ever really so? Why? Why are levers useful, 
since efficiency is less than 1 ? Do you ever use levers? 
Where and how? 



Mechanics 



15 



EXPERIMENT No. 5 

Question. — If a boy can carry half as much as a man, 
how would you arrange a load on a pole between them 
so that each will carry his share? 

Apparatus. — Two spring balances; rod; 10 kilogram 
weight. 




Directions. — Arrange the apparatus as shown in the 
diagram, letting balance M represent the man and 
balance B the boy. Move the weight W along the 
rod until the reading of M is twice that of B. Take 
the readings of the balances. In reading the balances 
make correction for the weight of the rod; this can 
be done by temporarily removing the weight. Meas- 
ure the distances AO and OC. Compute the value 

oi the tractions — and . 

B OC 



16 



Laboratory Manual in Physics 



Record your results in a table similar to the 
following : 

Results. — 



Force 
M 


Force 
B 


Distance 
AO 


Distance 
OC 


M+B 


AO : OC 















Discussion. — How does the ratio of the two forces M 
and B compare with the inverse ratio of their dis- 
tances from where the weight W is hung? State the 
relationship in the form of a proportion. The weight 
W holds the two forces M and B in equilibrium, and 
is known as their equilibrant. How does the equili- 
brant compare in value with the sum of the two 
parallel forces? Is any work done in this experiment? 
How? Do the readings of the balances change if you 
raise the apparatus uniformly upward or move it 
sideways? 

If you invert the apparatus, letting the two balances 
hang down and the 10 kilograms act upward, what 
weights on the two will balance it? When you shovel 
coal, do you pull up with your left hand as hard as you 
push down with your right? Why? 

Problem. — Where must a load of 200 pounds be 
placed on a stick 10 feet long, if the boy who holds 
one end is to support 60 pounds? 



Mechanics 
EXPERIMENT No. 6 



17 



Question. — When a girl weighing a hundred pounds 
sits in a hammock, is the strain on each hook a hundred 
pounds, or is it more or less? 

Does the amount the hammock sags affect the 
strain on the hooks? 

Apparatus. — Two spring balances; weight of 20 or 
25 pounds; cord. 




Directions. — Find the value of the weight in pourds 
and then arrange the apparatus as shown in the 
diagram. Take the readings of the balances A and 
B. Now lengthen the cord connecting A and B so 
that it will sag more, and again take the readings of 
the balances. 

Results. — Tabulate your results obtained under the 
first and second trials, and answer the questions asked 
above. 

Discussion. — The force W holds in equilibrium the 
two forces A and B and is known as their cqnilibrant. 



18 



Laboratory Manual in Physics 




Suppose in place of the two forces A and B, we sub- 
stitute just one force to balance the force W; such a 
force would be known as the resultant of A and B. 
r To find this resultant, 

place a stiff piece of paper 
behind the juncture of the 
cords and get the exact 
directions of the forces A , 
B, and W. Now r using a 
convenient scale (e.g. }/L in. 
= 1 lb.), lay off on OA, 
OB, and OW, the values of A, B, and W, respectively. 
Complete the parallelogram as shown in the diagram 
and draw the diagonal OC. OC represents the resul- 
tant of OA and OB. Measure the diagonal and 
multiply its length by the scale number to find its 
numerical value. 

How does the magnitude and direction of the 
resultant compare with the magnitude and direction 
of the equilibrant W? 

What three forces are in equilibrium here? Do the 
lines that represent three forces in equilibrium form 
a triangle? If you knew the weight of the girl in the 
hammock, what measurements would you make on 
the hammock to find the pull on the ropes? 

Is any work done by the forces in this experiment? 
Why? 

Under what conditions will the tension on each 
rope be half the weight of the girl? Is it possible to 
stretch a rope so tight that it will be truly straight 
and horizontal? Why? 



Mechanics 19 

EXPERIMENT No. 7 

Question. — Where will water pipes tend to burst 
first on account of water pressure, in the basement or 
at the top of the building? 

What is the change in pressure per vertical foot? 

Apparatus. — Pressure gauge. 

Directions. — Find the pressure of the water on the 
different floors of the school building by attaching the 
gauge to taps indicated by the instructor. If, while 
you are performing this experiment, some one should 
draw water from a faucet, the pressure would be 
decreased in the pipes throughout the building; there- 
fore leave the gauge attached at each tap for a minute 
and take the highest reading that you can get. Take, 
also, the vertical distances in feet between the taps. 

Results. — Tabulate the results obtained, and calcu- 
late the change in pressure per vertical foot. 

Discussion. — You can now answer the question as to 
where water pipes will tend to burst first. 

How high could you run a water pipe in your city 
before reaching an elevation where there would be 
no pressure at all? 

Does a stand pipe have to be constructed of the 
same strength from bottom to top? Why? 

How is a dam constructed? 

Why are railroad water tanks made flat and of 
large diameter instead of tall and of smaller diameter? 



20 Laboratory Manual in Physics 

EXPERIMENT No. 8 

Question. — How much does the air in the laboratory 
weigh? 

Apparatus. — Meter stick; bottle with stopper, 
tubing and pinch-cock; air pump; c. c. graduate ; large 
vessel of water. 

Directions. — Measure the length, width, and height 
of the laboratory and calculate its volume in liters 
(1 liter = 1000 c. c). To get the weight of a liter of 
the air in the laboratory proceed as follows. See that 
the bottle and tubing are perfectly dry inside. Place 
a little vaseline around tubing and stopper to make the 
bottle air-tight. Get the weight of the bottle with 
attachments in grams. Extract from the bottle as 
much air as possible and close the pinch-cock securely. 
Again weigh and calculate the weight of air removed. 

Place the bottle with its connections completely 
under water, and open the pinch-cock allowing water 
to flow in and take the place of the air which was 
removed. With the end of the tube still under water, 
hold the bottle in a horizontal position on the surface 
of the water so that the water inside the bottle is on a 
level with the water in the vessel, and then close the 
pinch-cock. Why must the bottle be held in this 
position when the pinch-cock is closed? Measure 
the volume of the water in the bottle in cubic centi- 
meters. This will, of course, be equivalent to the 
volume of the air which was extracted. Knowing the 
weight of air extracted in grams and its volume in 
cabic centimeters, calculate the weight of a liter of air. 



Mechanics 



21 



Results. — Record all data obtained and calculations 
made, and express the weight of the air in the room 
in both kilograms and pounds. 

Discussion. — Is the weight of the airinthe laboratory 
the same at all times? Why? 

Why does not your body notice this great pressure 
of the air? 



EXPERIMENT No. 9 

Question. — If a force of 50 pounds is exerted at the 
handle of the hydraulic press in the laboratory what 
pressure is exerted by the large piston? 

Apparatus. — Hydraulic press; spring balance; 
calipers. 

PART I 



OR 



C 



B 




An 



X 









Directions. — First calculate the downward pressure 
that is exerted by the piston A if a force of 50 pounds 
is applied to the handle D. To do this, measure care- 



22 Laboratory Manual in Physics 

fully the lever arms OC and OD from centers of pivots 
at and C and consult your text for a solution of 
problems in connection with levers of the second class. 
Now caliper the pistons A and B, and calculate the 
areas of their ends. (Area = 34 x D 2 ). Determine 
the upward pressure exerted by the large piston B 
by applying the following law. The force exerted by 
the small piston is to the force exerted by the large piston 
as the area of the small piston is to the area of the large 
piston. 

PART II 

The results obtained in Part I by calculations from 
dimensions of the hydraulic machine are theoretical. 
Let us now find what pressure is obtained by the 
actual working of the machine. Place a block above 
the large piston to prevent it from moving upward. 
Pump water into the press until a pull of 50 pounds on 
the spring balance attached to the handle is necessary 
to force more water into the machine. The pressure 
exerted by the large piston is obtained by reading the 
gauge, G. If the gauge does not register the total 
pressure but reads " Pounds per square inch" or 
"Atmospheres" the total pressure in pounds can 
easily be computed. 

Discussion. — What are the causes of the difference 
between the results obtained in Part I and Part II? 
Name the different places at which friction occurs. 
Do the weights of the lever and pistons have any 
effect on the actual results? If so, what is the effect 
of each? Is the actual pressure exerted upward by 



Mechanics 



23 



the large piston really quite the same as that indicated 
by the gauge? Why? Explain why the pressure 
exerted by the hydraulic press is multiplied to such 
an extent. Consult a reference book for a discussion 
of Pascal's Law relative to liquid pressure. 

Name other appliances in which the principle of 
the hydraulic machine is made use of. 

EXPERIMENT No. 10 



Question. — If the gas company 
were to double the pressure on 
the tank supplying the mains, 
what effect would it have on the 
volume of the confined gas? 

Apparatus. — Boyle's appara- 
tus; mercury; illuminating gas; 
barometer. 

Directions. — In the apparatus 
shown in the diagram the tube a 
is filled with illuminating gas. 
Move the tube b until the mercury 
stands at the same level in both 
tubes. Evidently the only pressure 
now on the confined gas is that of 
the atmosphere, since the two mer- 
cury columns balance each other. 
How much is this atmospheric 
pressure? To determine this read 
the barometer. The barometer shows what length 
of mercury column is balanced by the atmosphere. 




24 Laboratory Manual in Physics 

Record the volume of the confined gas. This volume 
may be expressed in inches (or centimeters) since the 
diameter of the tube a is the same throughout. Also 
record the pressure upon the gas. as indicated by the 
barometer. This pressure is expressed in so many 
inches (or centimeters) of mercury. 

Now double the pressure upon the gas by raising 
the tube b until the difference in level between the 
columns of mercury is equal to the reading of the 
barometer. The pressure on the confined gas is now 
two atmospheres. Record this together with the 
volume of the gas. 

Results. — Tabulate in a neat form data obtained. 

Discussion. — What effect has doubling the pressure 
upon the volume of the confined gas? 

While performing this experiment would the results 
be effected if the temperature of the room changed 
materially? Why? 

Robert Boyle first discovered this relationship 
between pressure and volume of gas which you have 
just proved, and other physicists have shown that it 
holds good for all gases. Consult your text book for a 
statement of Boyle's Law. 

Problem. — The air in the air dome of a fire engine 
pump is at atmospheric pressure when the pump is 
not working. Suppose when the pump is working, 
the air in the dome is reduced to one-fourth of its 
original volume, what pressure does it exert? (One 
atmosphere = 15 lb. per sq. in.) 



Mechanics 



25 



EXPERIMENT No. 11 

Question. — Which weighs the more; a wooden 
bridge containing 500 cubic feet of spruce, or an 
iron bridge containing 100 cubic feet of iron? 

Apparatus. — Rectangular blocks of spruce and iron. 

Directions. — First find the density of spruce and of 
iron. By density is meant the weight of a unit 
volume. One way of expressing it is in grams per 
cubic centimeter. Measure the length, breadth, and 
thickness of the blocks and compute their volumes in 
cubic centimeters. Also find their weights in grams. 
Calculate the weight of one cubic centimeter of each 
block. Since one cubic centimeter of water weighs 
one gram, and one cubic foot of water weighs 62.5 
pounds, you can readily compute the weight of a cubic 
foot of spruce and of iron. 

Results. — 





Length 


Breadth 


Thickness Volume 


Weight 


Density 


Spruce 














Iron 















Weight 1 cu. ft. iron = 
Weight 1 cu. ft. spruce = 
Weight of spruce bridge = 
Weight of iron bridge = 



26 Laboratory Manual in Physics 

Discussior. — Can the Cubans make rafts of ebony? 
Why? Why are fishing bobbers made of cork? Why 
is lead placed in the keel of a boat? 

Problem. — Thomas Edison was recently presented 
with a cube of copper one foot on each edge. Could 
he carry it? Compute the weight. 

EXPERIMENT No. 12 

Question. — What is the specific gravity of the milk 
and cream obtained from your milkman? How do 
your results compare with those obtained by others 
of your class? 

Apparatus. — Milk; cream; specific gravity bottle. 
Directions. — The specific gravity of milk means its 
weight divided by the weight of an equal volume of 
water. Weigh the empty bottle when perfectly dry. 
Fill the bottle half way up the neck with water, drop 
in the stopper, and allow the hole in the stopper to 
become filled with water. Dry the outside of the 
bottle and again weigh to find the weight of the water. 
In the same way find the weight of the bottle full of 
milk; also full of cream. 

Results. — Weight of water = 

Weight of milk = 

Weight of cream = 

Specific gravity of milk = 

Specific gravity of cream = 

Results obtained by other 

members of class : Milk = 
Cream = 



Mechanics 27 

Discussion. — 

Why does cream rise to the top of milk? 
How does a cream separator work? 
In which can you float more easily, salt or fresh 
water? Why? 

How are submarines made to rise or sink? 

EXPERIMENT Xo. 13 

Question. — Does the lead sinker on your fishing line 
pull on the line more when it is out of the water than 
when it is in the water? If so, how much more? Use 
results obtained for finding the specific gravity of lead. 

Apparatus. — Piece of lead; balance; vessel of water. 

Directions. — Suspend the piece of lead from the left 
side of the balance by means of fine thread and find 
its weight. Xow hang the piece of lead in water and 
find its weight in water. Compute its loss of weight 
in water. 

How can these results be used to find the specific 
gravity of lead? By specific gravity of a substance 
is meant its weight divided by the "weight of an equal 
volume of water. The piece of lead, of course, dis- 
places its own volume of water, and the weight of this 
water displaced, as Archimedes first discovered, is 
equal to the loss of weight of the lead in water. There- 
fore, if you know the weight of the piece of lead in 
air and its loss of weight in water you can find the 
specific gravity of lead. 

Weight in air 



Specific gravity 



I . ss of weight in water 



28 Laboratory Manual in Physics 

Results. — 

Weight of lead in air = 

Weight of lead in water = 

Loss of weight of lead in water = 
Specific gravity of lead = 

Discussion. — How would you perform an experiment 

to prove Archimedes' principle that a body immersed 

in water is buoyed up by a force equal to the weight of the 

water displaced'? 

Problem. — If you can just float in water with your 

nose out what is your volume? 

EXPERIMENT No. 14 

Question. — What is the efficiency of the water motor 
in the laboratory? 

Apparatus. — Water motor; pressure gauge; two 
spring balances; brake belt; speed indicator. 

Directions. — To obtain the work put into the motor 
it will be necessary to get the pressure of the water in 
pounds per square inch by means of the gauge G 
connected to the supply pipe, also the quantity of 
water in cubic inches flowing through the motor in a 
given time and caught in the vessel V. 

To obtain the work gotten out of the motor it is 
necessary to make use of a brake consisting of two 
spring balances A and B and a friction belt passing 
under the pulley P. Raise the rod supporting the 
balances until the motor slows down to its ordinary 
working speed. If the motor rotates in the direction 



Mechanics 



29 



indicated by the arrow the belt will pull harder on B 
than on A. The difference between the readings of 
the balances measures the pounds pull of the motor 
on the belt. 




A r 



i y\ 



v 



One student should take care of the speed indicator; 
a second student, the balances; and a third, the gauge 
and flow of water. 

Before starting the motor disconnect the belt from 
the balance A. When the motor has reached full 
speed replace the belt on balance A. At the word 
"Go" from the student watching the speed indicator, 
place the empty vessel V under the outlet and let run 
for a short time, say two minutes. Note the number 
of revolutions, and during the entire time observe the 



30 Laboratory Manual in Physics 

balances and gauge in order to get their average 

readings. Determine the volume of the water in 

cubic inches. The input, or work done on the motor, 

is called fluid work and depends upon the pressure of 

the water and the volume of flow. 

Fluid work = Pressure X volume 

Since the pressure is in pounds per square inch and the 

volume in cubic inches, the volume must be divided 

by 12 (1 ft. = 12 in.) in order to obtain the work 

expressed in foot-pounds. Therefore 

T ^ ,„ . N (volume cu. in.) 
Input = Pressure (lb. per sq. in.) X — 

The output, or work done by the motor is equal to 
the pounds pull on the belt multiplied by the distance 
through which this pull acts. During one revolution 
this pull acts through a distance equal to the circum- 
ference of the pulley. With a pair of calipers measure 
the diameter of the pulley and calculate the circum- 
ference in feet. The circumference multiplied by the 
number of revolutions gives the total number of feet 
through which the pull acts. The product of the 
pounds pull by the distance in feet gives the output 
of the motor in foot-pounds. 

Determine the efficiency of the motor. 

• Output 

Efficiency = -; 

Input 

Results. — 

Input: 

Pressure of water = 

Volume of water = 

Work put into motor = 



Mechanics 3 1 

Output: 

Pounds pull (B— A ) = 

Circumference of pulley = 
Number of revolutions = 
Total distance = 

Work done by motor = 
Efficiency = 

Discussion. — To what is the loss in a water motor 
due? Is the pressure of the water at the outlet the same 
as at the inlet? Where does the loss in pressure occur? 
Instead of expressing the input or output in foot- 
pounds of work, we may express them in the form of 
mechanical power, or foot-pounds of work per second. 
And so the efficiency may be expressed as the ratio 
of power output to power input, or 

_„ . Power output 

Efficiency = ~ : 

rower input 

Since the work in and work out were performed in the 
same time the ratio of powers is equal to the ratio of 
works. In speaking of the output of a motor which 
term is usually applied, "foot-pounds of work" or 
"power"? 

Calculate the delivered horse-power of the motor 
from results obtained (1 horse-power = 550 foot- 
pounds per second). 



32 Laboratory Manual in Physics 

EXPERIMENT No. 15 

Question. — Which makes the best lining for a fireless 
cooker; an air space, excelsior, felt, or mineral wool? 

Apparatus. — Four calorimeters, or tin cans, with 
covers; four thermometers; excelsior; felt; mineral 
wool; pan with clamps. 




Directions. — First heat a large kettle of water. 
While the water is coming to a boil, pack one can with 
excelsior, one with felt, and one with mineral wool. 
The fourth can is used with just the air in it. Arrange 
a thermometer in each can with the bulb in the center 
of the can and the stem passing through the hole in 
the cover. Clamp the cans in the pan as shown in the 
diagram. Now pour boiling water into the pan until 
the cans are about three-fourths submerged, being 
careful not to get any water in the cans. Let stand 
until ten minutes before the close of the laboratory 
period; then take the readings of the thermometers. 
Remove the cans, being careful not to let them tip 
over in the water, and empty the pan. 



Heat 33 

Results. — Record the final temperatures and arrange 
the different substances in the order of their conduc- 
tivity. 

Discussion. — Why do storm windows keep a house 
warmer? Why are steam pipes often covered with 
asbestos? Why does a thermos bottle retain the heat 
longer than a fireless cooker? Why is a wool blanket 
warmer than a cotton blanket of the same weight? 

Name a dozen poor conductors of heat; a dozen 
good conductors. 

EXPERIMENT No. 16 

Question. — In a kettle of boiling water, which is 
hotter, the water or the steam above the water? 

At what temperature does water boil in your 
locality? 

Apparatus. — Glass flask; thermometer reading to 
tenths; two-hole rubber stopper; bent glass tube. 

Directions. — Be very careful with the thermometer 
used in this experiment as it is of a higher grade than 
is ordinarily employed in the laboratory. Arrange 
the apparatus as shown in the diagram with the bulb 
of the thermometer just beneath the surface of the 
water. When the wjater is boiling freely take the 
reading of the thermometer, estimating to tenths of 
degrees. Boil the water faster or slower and see what 
difference it makes in the boiling point. Now raise 
the thermometer above the water and take the temper- 
ature of the steam. 



34 



Laboratory Manual in Physics 



MJ 




Results. — Temperature of boiling water = 
Temperature of steam = 

Elevation of (your locality) = 

Discussion. — Will water boil at the same tempera- 
ture on the top of a high mountain as it will at the 
level of the sea? Why? 

When boiling vegetables will they get done any 
sooner by boiling the water faster? 

Which do you think is a better way to cook vege- 
tables, in boiling water or in steam? Why? 



Heat 
EXPERIMENT No. 17 



35 



Problem. — How much does an iron bridge 100 
feet long change in length if the range in tempera- 
ture is from 40° C. in summer to— 40° C. in winter? 

Remarks. — In order to work this problem, it will be 
necessary to first find the fraction of its length which 
a piece of iron expands on being heated 1° C. 

Apparatus. — Expansion frame; iron rod; boiler; 
thermometer; telegraph sounder; one cell. 





Directions. — Measure the length of the iron rod in 
centimeters and place it in the steam jacket J shown 
in the diagram. Push the thermometer T down until 
it touches the rod, being careful not to break the 
thermometer. Connect the telegraph sounder S and 
the cell in series with the frame. See that the iron 
rod rests firmly against the back stop K. If the 
micrometer screw M is turned up until it touches the 
iron rod, the electric circuit will be completed and the 
sounder will click. (Caution. — Turn up the micro- 
meter carefully so that only sufficient contact is made 
to cause the sounder to click; otherwise you will 



36 Laboratory Manual in Physics 

strain the instrument.) Note that the micrometer 
reads in hundredths of millimeters. Adjust K so that 
the micrometer will stand at zero when the sounder 
clicks. After this adjustment do not allow the jacket 
to turn, otherwise it will affect the reading of the 
micrometer. Now turn back the micrometer so that 
it will be out of the way when the rod expands. Take 
the reading of the thermometer which will give the 
temperature of the cold rod. Pass steam through the 
jacket and continue to heat the rod a half minute 
after the thermometer has ceased to rise. Take the 
temperature of the hot rod. Now turn the micro- 
meter until the sounder clicks. Note by the 
micrometer how much the rod expanded. 

Results. — Fraction of its length which iron rod 

amount of expansion 

expanded = — . r — ; 73 — = 

length when cold 

This divided by the change in temperature gives the 
fraction of its length which the iron rod expanded for 
a change of 1° C. Express this result in the form of a 
decimal. This result is known as the coefficient of 
linear expansion of iron. 

The iron bridge will expand this fraction of its length 
for a change of 1° C. Calculatehow much it willexpand 
for the change of temperature given in the problem. 

Discussion. — In building a railway, why are spaces 
left between the rails? 

Why are steam boilers put together with red-hot 
rivets? 

Why do telegraph wires "sing" more in winter than 
in summer? 



Heat 37 

EXPERIMENT No. 18 

Question. — If a liter (1 kilogram) of water at 20° C. 
in an open kettle takes ten minutes to come to a boil, 
how long will it have to boil to change it all into vapor? 

Remarks. — The amount of heat required to raise the 
temperature of 1 gram of water 1° C. is taken as the unit 
of heat and is called the calorie. Evidently to bring 
the kilogram of water to the boiling point, 100° C, 
requires 1000 grams X (100° - 20°) = 80,000 calories. 
In other words 80,000 calories of heat were given up by 
the flame to the water in ten minutes. In order to 
find how long it will take to change the boiling water 
into steam it will be necessary first to determine by 
experiment how many calories are required to change 
1 gram of boiling water into steam. 

Apparatus. — Flask with water trap attached ; calori- 
meter; thermometer. 

Directions.— Have the flask about one-half full of 
water and start it to heating. Empty the water trap if 
it contains much water. Weigh the calorimeter 
and put into it exactly 500 grams of cold water. Take 
the temperature of the water. Place a screen between 
the boiler and the calorimeter to prevent heat from 
the flame reaching the calorimeter. When steam is 
given off freely from the boiler introduce sufficient 
steam into the water to raise its temperature to about 
35° C, at the same time constantly stirring the water 
with the thermometer. Before turning off the burner, 
remove the calorimeter, stir, and take the final tern- 



38 Laboratory Manual in Physics 

perature. Again weigh to find the amount of steam 
condensed in the water. 




a. The number of calories of heat taken up by the 
cold water is evidently the weight of the water 
(500 gm.) multiplied by its rise in temperature. Part 
of this heat was given up by the steam in being con- 
densed and part by the condensed steam in being 
lowered to the final temperature. 

b. The number of calories of heat given up by the 
steam after it was condensed is equal to the weight 
of the steam multiplied by its fall in temperature. 

Subtracting b from a we have the amount of heat 
given up by the steam in being condensed. This 
divided by the weight of the steam gives the amount 
of heat given up by 1 gm. of steam in being condensed. 



Heat 39 

Results. — 

Weight of cold water = 

Amount of heat taken up by water (a) = 
Weight of steam = 

Amount of heat given up 

to water by condensed steam (6) = 
Amount of heat given up 

by steam in being condensed (a — b) = 
Amount of heat given up by 1 

gm. of steam in being condensed = 
Discussion. — The result just obtained is of course 
the same as the amount of heat required to change 
one gram of boiling water into steam. This is known 
as the Heat of Vaporization of Water, You can now 
estimate how long it w^ill take to entirely vaporize the 
liter of water referred to in the above problem. 
Explain how a steam heating plant operates. 
Why are burns from steam more painful and inju- 
rious than those from boiling water? 

In hot dry atmospheres, like that of Mexico, water 
is cooled by placing it in porous earthenware jars or 
canvas bags. Explain. 



40 Laboratory Manual in Physics 



EXPERIMENT No. 19 

Question. — What is the temperature at which dew- 
will form today? Compare your result with those 
obtained by other students on other days. 

Apparatus. — Thermometer; calorimeter; ice; water. 

Directions. — Place about two inches of water in the 
calorimeter. Add finely crushed ice to the water, a 
very little at a time, stirring continually with the 
thermometer. Watch closely for the first appearance 
of moisture on the calorimeter. Since the breath 
contains more moisture than the air of the room, be 
very careful not to breathe against the vessel. When 
the dew first appears, take the reading of the ther- 
mometer. Try several times, wiping off the dew, 
adding a little warm water, and then more ice. The 
object is to find the highest temperature at which there 
is the slightest appearance of moisture. 

Results.— Tabulate the temperature and date 
together with results gotten by other students. 

Discussion. — The temperature at which the water 
vapor in the atmosphere becomes saturated and begins 
to condense is known as the dew point. Is the dew 
point in winter higher or lower than in summer? 
What is frost? Do "Jack Frost's pictures" appear on 
the outside or inside of windows? Why? Do they 
appear more frequently when it is very cold? Why? 
On the kitchen windows, or those of the bedroom? 
In heated houses or cold sheds? Why? 



Heat 41 



EXPERIMENT No. 20 

Question. — Will a vessel of water come to a boil 
sooner when the cover is left on than it will when the 
cover i9 off? Why? 

PART I 

Apparatus. — Two-quart pail with loose cover, or a 
teakettle; plate burner; thermometer. 

Directions. — Put a given amount of water, say a 
quart or a liter, at a given temperature into the vessel, 
and, leaving off the cover, note the time necessary to 
bring the water to a boil. Repeat the experiment 
with the cover on, having all other conditions the same. 

Results. — Tabulate your results for both cases as 
to amount and temperature of water and time 
consumed. 

PART II 

Apparatus. — Two barometer tubes; mercury; cup; 
pointed bent tube with rubber bulb attached. 

Directions. — With the assistance of the instructor 
fill the tubes with mercury and invert in the cup of 
mercury. Note that the mercury stands at the same 
level in both tubes. What holds the mercury up in 
the tubes? Introduce a little water into the tube 
B, being careful not to let in any air, and note the 



42 Laboratory Manual in Physics 




difference in the heights of the mer- 
cury in the two tubes. The reason 
the mercury falls in the tube B 
is because the water evaporates until 
the upper part of the tube is filled 
with saturated water vapor, exerting 
a downward pressure on the mercury. 
Now raise the temperature of the 
water by holding a gas flame within 
an inch of the tube. {Caution. — Do 
not let the flame touch the glass.) 
Does this cause more water to evapo- 
rate? How do you know? Would 
you conclude that for a given tem- 
perature a given amount of water will 
evaporate in order to produce satu- 
ration in the upper part of the tube, 
and that when saturation is reached 
evaporation will cease? 

Discussion. — You are familiar with 
the fact that when water evaporates 
from the hand, the hand is cooled. 
You are now ready to explain fully the 
effect produced by leaving off the lid 
of a kettle while the water is coming 
to a boil. 

If a kettle boiled long enough to 
saturate all of the air in the room, 
would further evaporation take place 
from the kettle? 



Heat 
EXPERIMENT No. 21 

Question. — Why is it that an 
egg cannot be boiled hard on the 
top of a high mountain? 

Apparatus. — Air pump; tall 
receiver; glass beaker; ther- 
mometer. 

Directions. — Fill the beaker 
about one-third full of water and 
bring to a boil. Note the tern 
perature of the boiling 
water. Transfer the 
beaker to the air pump 
and arrange the appa- 
ratus as shown in the 
diagram, with the ther- 
mometer passing 
through a stopper in the 
top of the receiver and 
the bulb of the ther- 
mometer in the water. 
Be very careful not to 
break the thermometer. 
Extract air until the 
water begins to boil. 
Note the temperature, 
also the reading of the 
pressure gauge attached 
to the pump. Repeat 
the operation every 



43 




44 Laboratory Manual in Physics 

minute or so until a half dozen or more results have 
been obtained. 

Results. — Tabulate your results showing the vary- 
ing temperatures and pressures at which the water 
boils. Calculate the change in pressure necessary to 
produce a change of 1° C. in the boiling point of water. 

Discussion. — How would you devise a cooking 
utensil that would boil eggs on top of a high mountain? 

When an engine boiler gives way, why does the 
water sometimes change instantaneously into steam 
with great violence? 

Problem. — On the top of Pike's Peak the barom- 
eter stands commonly at 17.79 inches. At what 
temperature does the water boil? 

EXPERIMENT No. 22 

Problem. — How much ice is needed to cool a liter of 
water at 40° C. to 5° C? Test it and compute the 
heat of fusion of ice. 

Apparatus. — -Calorimeter or tin can; ice; ther- 
mometer. 

Directions. — Weigh the dry calorimeter. Put into 
it 1 liter (1 kilogram) of water heated to a little above 
40° C. When the water reaches 40° drop in two good 
sized handfuls of cracked dry ice. Stir continually 
with the thermometer. When the temperature 
reaches 5°, quickly remove the remaining ice. Weigh 
again to obtain the amount of ice intrduced. 

The heat unit in the metric system is the gram- 
calorie, i.e., the amount of heat required to raise the 



Heat 45 

temperature of 1 gram of water 1° C. The number of 
gram-calories required to melt 1 gram of ice is known 
as the heat of fusion of ice. 

Results. — Calculate the number of gram-calories 
given up by the 1000 grams of water in cooling from 
40° to 5°. This heat was evidently used, first, to 
melt the ice, and then to raise the temperature of 
the ice water from 0° to 5°. Calculate the heat 
required to raise the ice water to 5° by multiplying 
the weight of the ice (or ice water) by 5. Subtract- 
ing this from the amount of heat given up by the liter 
of water leaves the amount of heat required to melt 
the ice. This divided by the weight of the ice gives 
the number of gram-calories of heat required to melt 
1 gram of ice; that is, the heat of fusion of ice. 

Discussion. — Explain why a large lake that freezes 
over in winter prolongs the spring in the locality. 
Explain the action of an ice cream freezer. 

Why do farmers sometimes place tubs of water 
in cellars to prevent vegetables from freezing? 



EXPERIMENT No. 23 



Question. — How much heat is absorbed by an 
aluminum kettle having the temperature of the room 

hen it is filled with water at 60° C? Test it and 
: nnpute the specific heat of aluminum. 

Apparatus. — Aluminum kettle; thermometer; ves- 

! in which to heat water. 



46 Laboratory Manual in Physics 

Directions.— Weigh the aluminum kettle in grams. 
Note the temperature of the room and set the kettle 
in a place where it will retain this temperature. Heat 
sufficient water in another vessel to about 60° C. 
Take the temperature of the water. The next step 
must be made quickly. Pour enough of the water 
into the aluminum kettle to almost fill it, and stirring 
with the thermometer, quickly note the final temper- 
ature, which is of course the temperature of the kettle. 
Again weigh to obtain the amount of water used. 

By the specific heat of aluminum is meant the 
amount of heat required to raise the temperature of 
1 gram of aluminum 1° C. The amount of heat given 
up by 1 gram of water in cooling 1° C. is taken as the 
unit of heat, and is known as a gram-calorie. 

Results. — The weight of the water multiplied by 
its fall of temperature is equal to the number of gram- 
calories which it gives up to the aluminum kettle. 
Dividing this by the rise in temperature of the kettle 
will give the gram-calories required to raise the 
temperature of the kettle 1°. From which you can 
determine the amount of heat required to raise 1 gram 
of aluminum 1°; which is the specific heat of aluminum. 

Discussion. — Examine a table of specific heats and 
compare the specific heat of other substances with that 
of water. Why do hot water plants produce such 
even temperatures? 

Why do inland towns have a greater range of tem- 
perature than sea coast towns? 

Why is a hot water bottle bettef than a hot stove 
lid to keep your feet warm for the night? 



Heat 



47 



EXPERIMENT No. 24 

Question. — How much heat is produced by the 
combustion of one cubic foot of the gas supplied by 
your local gas company? 

Apparatus. — Gas meter; water jacket; two ther- 
mometers (Fahrenheit); Bunsen burner; vessel in 
which to catch water. 




Directions. — As shown in the diagram, water flows 
in at the bottom of the water jacket and out at the 
top. The hot gases from the burner pass through 



48 Laboratory Manual in Physics 

tubes surrounded by water and give up their heat to 
the water before passing out at the bottom of the 
apparatus. Thermometers placed at the bottom and 
top of the water jacket indicate the change in temper- 
ature of the water. By measuring the amount of 
water flowing through and its rise in temperature 
while one cubic foot of gas is consumed, the heat of 
combustion of the gas may be determined. 

Light the burner. To produce the best results do 
not have the flame too high, and adjust the burner so 
as to give it more air than usual, making the flame 
rustle when it burns. Place the burner under the 
calorimeter, turn on the water and let the apparatus 
run until the thermometers remain stationary. Now 
place the vessel V under the outlet and at the same 
time note the reading of the gas meter. Let run until 
exactly one cubic foot of gas has been consumed and 
at the same time shut off the water. Careful obser- 
vation should be made of the thermometers during the 
experiment to obtain their average readings. Take 
the weight or measure of the water passed through in 
pounds. Calculate the amount of heat taken up by 
the water, bearing in mind that 1 B. T. U. is the 
amount of heat that will raise the temperature of 1 
pound of water 1° F. The result is the heat of com- 
bustion of 1 cubic foot of the gas supplied to the 
laboratory. 

Results. — Rise in temperature of water = 

Weight of water = 

Heat of combustion per cubic foot = 



Heat 



49 



Discussion. — How much does your local company 
charge for gas per thousand feet {i.e., cubic feet)? 
Calculate how much it costs you to heat 6 pints 
{i.e., 6 pounds) of water from 40° F. to the boiling 
point if you use a burner and teakettle having a com- 
bined efficiency of 52 per cent. 

The heat of combustion of coai may be found by 
burning it in a suitably constructed water-jacket. 
For average coal it is 15,000 B. T. U. per pound. If 
the furnace in your house burns 100 pounds of coal 
a day how many B. T. U. are liberated in the house if 
the furnace has an efficiency of 50 per cent. 

EXPERIMENT No. 25 



Question. — What is the thermal efficiency of an 
ordinary teakettle? 

Apparatus. — Bunsen burner; teakettle; gas meter; 
Fahrenheit thermometer. 




Directions. — Put into the teakettle 4 pounds of 
water, noting the temperature of the water. Heat 



50 Laboratory Manual in Physics 

this over the same gas burner used in Experiment No. 
24 until 1 cubic foot of gas is consumed. Again take 
the temperature of the water. 

Results. — Calculate the number of B. T. U. taken 
up by the water. (For definition of B. T. U. see the 
text book.) The number of B. T. U. supplied by 
the combustion of the cubic foot of gas has already 
been determined in Experiment No. 24. 

You can calculate the efficiency of the kettle, which 

is the ratio of the useful heat got out to the total heat 

put in; or 

™ ii?«; ■ Heat out (B.T.U.) ~ 

Thermal Efficiency = — ; — /p ^ TT , = % 

Heat in (B.T. U.) /u 

Discussion. — Can you think of a way of increasing 
the efficiency of a teakettle? Would a teakettle with 
a highly polished bottom be more efficient than one 
with a smoked bottom? Why? 

If you wished to heat 3 quarts of water, which 
would be more efficient, to use a 4-quart or an 8-quart 
kettle? Why? 

Problem. — An engine with its boiler consumes 192 
pounds of coal per hour and deyelops 96 horse-power. 
What is its efficiency? (1 B. T. U. = 778 foot- 
pounds. Heat of combustion of coal = 15,500 
B. T. U. per pound.) 



Electricity and Magnetism 
EXPERIMENT No. 26 



51 



Question. — Does a cell lose its strength if continu- 
ously connected? Test a dry cell; a gravity cell. 
Which form is better for door bells? Which for 
telegraph lines? 

Apparatus. — Dry cell; gravity cell; galvanometer. 

Directions. — Connect the dry cell to the galvano- 
meter and take readings every two minutes for ten 
minutes. Test the gravity cell in the same way. 
Examine the construction of a gravity cell, also the 
half of a dry cell sawed lengthwise. The dry cell is 
not really "dry" but is kept moist by a solution of 
sal ammoniac. Note how it is sealed at the top in 
order to keep the cell moist. Consult your text book 
for a discussion of polarization. 

Results. — 





Reading of Galvanometer 


min. 


2 min. 


4 min. 


6 min. 


8 min. 


10 i ; •!. 


Dry cell 














Gravity cell 















Discussion. — Do either of the cells become polarized? 

Which is suited for "open circuit" work such as 
ringing door bells or running gas engines? Which 
for "closed circuit" work such as telegraphing? 

Why not use the gravity cell for all kinds of work? 



52 Laboratory Manual in Physics 



EXPERIMENT No. 27 

Question. — What is the nature of the field about a 
magnet? 

Apparatus. — Two bar magnets; iron filings; blue- 
print paper; plate of glass. 

Directions. — Place on the table a bar magnet, and 
over this a plate of glass. Sift fine iron filings evenly 
on the plate, being careful not to use too many filings. 
Holding one corner of the plate, tap it gently with a 
pencil until the magnetic lines of force are well defined. 
Lift up the plate vertically from the magnet and place 
beneath it a piece of blue-print paper. Expose this 
to the sunlight about 20 seconds, then quickly place 
it in the sink and rinse thoroughly. When dry, bind 
it in your notebook. Repeat the experiment with two 
like poles separated about two inches with the 
magnets lying in the same straight line. Again, 
with two unlike poles. 

Discussion. — Are the lines about a bar magnet 
uniformly distributed or are there crowded places? 
What is the cause of this? 

Are the poles immediately at the ends of the bar? 

Do the lines cross each other or do they merge into 
one another? 

Which poles placed near each other show magnetic 
attraction? Which magnetic repulsion? 



Electricity and Magnetism 
EXPERIMENT No. 28 



53 



Question. — What determines the strength of an 
electro-magnet? 

Apparatus. — Soft iron rod; two spools of magnet 
wire; tacks; two cells; compass. 



jluml 




Directions. — Slip one of the spools of wire over the 
rod and connect to one of the cells. See how many 
tacks end to end you can get to hang on the end of the 
rod. In the same way try two spools connected with 
one cell and again two spools with two cells. 
{Caution. — When the two spools are used they must 
be placed on the rod in such a way that the current 
will pass around the rod in the same direction 
through both.) 

Test a coil of wire without the iron core and see if 
it possesses any magnetism. If it will not attract 
tacks, test it with a magnetic needle. 

Using a magnet needle, test the electro-magnet 
for polarity. 



54 Laboratory Manual in Physics 

Discussion. — What effect has increasing the number 
of turns of wire on the strength of the electro-magnet? 
Does doubling the number of turns double the 
strength? 

What effect has increasing the strength of the 
current? Is the magnetic strength proportioned to 
the current strength? 

Examine an electric bell and explain how it operates. 

Name some other instruments that make use of 
electro-magnets. 

EXPERIMENT No. 29 

Question. — What effect has the length, diameter, or 
material of a conductor upon its electrical resistance? 

Apparatus. — Frame containing 100 centimeters of 
No. 30 copper, 100 centimeters of No. 30 German 
silver, 100 centimeters of No. 24 German silver, and 
50 centimeters of No. 30 German silver; ammeter; 
voltmeter ; one storage cell or two dry cells ; wire gauge. 

Directions. — Connect the ammeter in series and the 

voltmeter in parallel with the 100 centimeters of No. 30 

German silver wire as shown in the diagram. The 

ammeter gives the current in amperes passing through 

the wire, and the voltmeter gives the fall of potential 

in volts. Read the amperes and volts to tenths. Be 

careful to leave the battery connected only long enough 

to take the readings of the meters in order not to 

decrease the strength of the battery. Calculate the 

resistance of the wire in ohms. By Ohm's Law : 

Volts 

Ohms = -7 

Amperes 



Electricity and Magnetism 



55 




In like manner determine the resistance of 50 centi- 
meters of the German silver No. 30 and compare it 
with the resistance of 100 centimeters of the same 
wire to show the effect of length. 

To show the effect of diameter, determine the 
resistance of 100 centimeters of German silver No. 24 
and compare it with the resistance of 100 centimeters 
of No. 30 German silver. See the wire table in the 
Appendix for the diameters of the wires. 

To show the effect of material determine the resis- 
tance of 100 centimeters of copper No. 30 and com- 
pare it with the resistance of the same size and 
length of German silver. 



56 Laboratory Manual in Physics 

Results. — 



Material 


Length 


Diameter 


Volts 


Amperes 


Resistance 



















































Discussion. — State the relation existing between the 
length of a wire and its resistance. 

State the relation existing between the diameter of 
a wire and its resistance. 

The resistance of German silver is how many times 
that of copper? 

Why are heavy copper cables used in the construc- 
tion of trolley wires? 

Of what material would you make a resistance coil 
for cutting down the current? 

Could the filament of an incandescent lamp be made 
of copper? Why? 



Electricity and Magnetism 57 

EXPERIMENT No. 30 

Question. — How can the electromotive force of a 
battery be increased? 

Apparatus. — Several dry cells; gravity cell; volt- 
meter. 

Remarks.— By the electromotive force of a battery 
is meant the force which the battery is able to exert 
in moving an electric current through a conductor. 
The volt is the unit of electromotive force. A cell 
having an E. M. F. of one volt can drive a current of 
one ampere through a conductor having a resistance 
of one ohm. The voltmeter is an instrument so 
constructed as to measure the electromotive force of 
a cell or battery. 

Directions. — Connect the voltmeter to one of the 
dry cells to see how much electromotive force it 
exerts. Now connect two cells in series and test with 
the voltmeter. Again with three cells in series. 
What effect has the size of a cell on its electromotive 
force? Test a dry cell of different size. Does a 
different kind of cell produce a different electromotive 
force? Test a gravity cell. 

Results. — 

E. M. F. of one dry cell = 

E. M. F. of two dry cells in series = 
E. M. F. of three dry cells in series = 
E. M. F. of dry cell of different size = 
E. M. F. of gravity cell = 

Discussion. — Just as two locomotives can pull or 
push twice as heavy a train as one locomotive, so two 



58 



Laboratory Manual in Physics 



cells in series can push twice as much current as one 
cell through the same resistance. 

If you test an electric bell, one dry cell will be 
found sufficient to ring it. Why, then, in the con- 
struction of some bell circuits, is it found necessary 
to use several cells in series? 



EXPERIMENT No. 31 

Question. — What makes an electric motor go? 
Apparatus. — D'Arsonval galvanometer; cell; resis- 
tance box. 




ooooo 
ooooo 



H 



Directions. — Note that the galvanometer as shown 
in the diagram consists of a permanent horseshoe 
magnet, between the poles of which is suspended a 



Electricity and Magnetism 59 

coil of wire. Connect the wires leading from the cell 
to the terminals of the coil of the galvanometer, 
introducing between the cell and the galvanometer a 
resistance of 500 or 1000 ohms depending upon the 
sensibility of the galvanometer. Why does the coil 
move in the direction it does and then come to rest in 
a certain position? You have already learned that 
when an electric current is passed through a coil of 
wire, the coil becomes a magnet with one of its faces 
a north pole and the other a south pole. So the mov- 
ing coil of the galvanometer becomes an electro- 
magnet and its poles are attracted by the unlike poles 
of the permanent horseshoe magnet. The coil takes 
up a position w T ith its north pole next to the south pole 
of the permanent magnet. 

Change the connections of the wires leading from 
the cell so as to reverse the direction of current in the 
coil. Explain the motion and final position of the 
coil. 

When the coil is set in motion it does not stop after 
making a half turn, but, on account of its inertia, its 
poles move past the unlike poles of the horseshoe 
magnet. Then the coil is stopped and brought back 
by the magnetic force and the twisting force of the 
ribbon by which the coil is suspended. If we could 
do away with the twisting force of the suspending 
ribbon could we produce a continual motion of rota- 
tion by reversing the current each half turn? Explain. 

Discussion. — The moving coil of an electric motor 
is mounted on a shaft so that continual motion of 
rotation is possible. The current is brought into this 



60 



Laboratory Manual in Physics 



by means of an arrangement which changes the 
direction of the current every half turn. Examine 
a toy motor and apply the principles learned in this 
experiment. 

EXPERIMENT No. 32 

Question. — In electro-plating with copper, how 
long will it take one ampere of current to deposit one 
gram of copper? 

Apparatus. — Copper plating bath with two loss 
plates and one gain plate; ammeter; rheostat; several 
cells. 




Directions. — Arrange the apparatus as shown in the 
diagram. {Caution. — Do not pass any current through 
the apparatus until the instructor has seen the con- 



Electricity and Magnetism 61 

nections) . The rheostat is a coil of resistance wire for 
regulating the amount of current and keeping it 
constant. In electro-plating, the metal is always 
deposited on the negative pole. Pass the current 
through the apparatus in such a direction that copper 
will be deposited on the middle or gain plate. 
Remove the middle plate, rinse in w^ater, dry over a 
gas flame, and weigh carefully to thousandths of a 
gram. Return the coil to the solution, turn on the 
current, and note the time and the reading of the 
ammeter. Keep the reading of the ammeter con- 
stant by means of the rheostat. Let run for an even 
number of minutes, say 20; then remove the gain 
plate, rinse and dry it very carefully so as not to 
remove any of the copper, and again weigh. 

From data obtained calculate how long it would 
take one ampere to deposit one gram of copper. 

Results. — 

Weight of copper deposited = 

Time of deposit = 

Number of amperes = 

Time one ampere will deposit one gram = 

Discussion. — If you had weighed the two loss plates 
at the beginning and end of the experiment you would 
have found that they had lost in weight just as much 
as the small plate gained. Thus the electro-plating 
solution maintains its strength. What would happen 
if you reversed the current while electro-plating? 

Problem. — In the copper refining plant at Great 
Falls, Montana, 90 tons of copper are deposited per 
day (24 hours). What strength current is used? 



62 Laboratory Manual in Physics 

EXPERIMENT No. 33 

Question. — What is meant by 'Tall of Potential?" 
Apparatus. — 110- volt current; three electric lamps; 
voltmeter. 




Directions. — Pass the current through the three 
lamps connected in series as shown in the diagram. 
It requires electrical pressure to force the current 
through the lamps. This pressure is measured by the 
voltmeter. Connect the terminals of the voltmeter 
to a and d to obtain the volts pressure required to 
drive the current through all three lamps. In like 



Electricity and Magnetism 63 

manner find the difference of electrical pressure 
between a and c for two lamps, and between a and b 
for one lamp. 
Results. — 

Volts pressure required for three lamps = 
Volts pressure required for two lamps = 
Volts pressure required for one lamp = 
Discussion. — Potential is only another expression 
for electrical pressure. Difference of Potential means 
difference of electrical pressure, and Fall of Potential 
means fall of electrical pressure. A voltmeter is used 
to measure the potential difference between any two 
points in an electrical circuit, just as pressure gauges 
are used to measure the difference in water pressure 
between any two points of a water pipe. The further 
away from the pumping station the greater the fall of 
pressure of the water in pounds per square inch, due 
to the resistance of the pipes. So the further the 
electric current goes in a conductor the greater the 
fall of potential in volts, due to the electrical resistance 
of the conductor. The greater the resistance the 
greater the fall of potential. Do the lamps used in 
this experiment all have the same amount of resist- 
ance? Why do not the lamps give light in this 
experiment? 



64 Laboratory Manual in Physics 

EXPERIMENT No. 34 

Question. — How much current is required to light 
an ordinary 16-candlepower carbon filament lamp? 
A 32-candlepower? 

What is the potential difference between the 
terminals of the lamp? Calculate the resistance of 
each. 

Apparatus.-- 110- volt circuit; 16-candlepower and 
32-candlepower lamps; voltmeter; ammeter. 




LINE 



Directions. — Connect the ammeter in series and the 
voltmeter in parallel with the lamp as shown in the 
diagram. {Caution. — Do not turn on the current 
without first showing the connections to the 



Electricity and Magnetism 



65 



instructor). The ammeter will give the current in 
amperes passing through the lamp, while the volt- 
meter will give the potential difference in volts 
between the terminals of the lamp. While testing 
one of the lamps have the other turned off. 

Since a potential difference of 1 volt will drive a 
current of 1 ampere through a resistance of 1 ohm, the 
resistance of the lamp in ohms can be calculated by 
making use of Ohm's Law: 



Amperes = 



Volts 



or 



Ohms 
Ohms = Volts -f- amperes 



Results.- 



Candlepower 
of Lamp 


Current 


Potential 
Difference 


Resistance 



















Discussion. — Examine the construction of the above 
lamps and note why one should have a higher resist- 
ance than the other. 

A street car running on a 550-volt circuit is to be 
lighted by twenty 110-volt 16-candlepower lamps. 
Make a diagram showing how these lamps should 
be connected. 



66 



Laboratory Manual in Physics 



EXPERIMENT No. 35 

Question. — Why is it better to connect house 
electric lamps in parallel? Find the resistance of 
two lamps in parallel and compare it with the resist- 
ance of one lamp found in the preceding experiment. 
Also the resistance of four lamps in parallel. 

Apparatus. — Four 16-candlepower lamps; 110-volt 
circuit; voltmeter; ammeter. 

Directions. — Connect the ammeter in series with 
two of the lamps, the lamps being in parallel, and con- 
nect the voltmeter across their terminals as shown in 
the diagram of the preceding experiment. {Caution. — 
Show connections to instructor before turning on the 
current.) Note the current in amperes passing 
through the lamps, also the potential difference in 
volts between the terminals of the lamps. In like 
manner test four lamps in parallel. 

Calculate the resistance of each combination of 
lamps by Ohm's Law as explained in Experiment 
No. 34. 

Results. — 





Current 


Voltage 


Resistance 


One lamp 








Two in 
parallel 








Four in 
parallel 









Electricity and Magnetism 67 

Discussion. — What is the effect of connecting lamps 
in parallel? Why is it advantageous to have house 
lamps connected in this way? 

Make a diagram showing how you would run the 
wires for a house of four rooms, each room having 
two lights. 



EXPERIMENT No. 36 

Question. — How many watts of power are required 
to light an arc lamp? 

Apparatus. — Arc lamp; voltmeter; ammeter. 

Directions. — Connect the ammeter in series and the 
voltmeter in parallel with the arc lamp. (Caution.—* 
Do not turn on the current until connections have 
been shown to the instructor. As soon as the lamp 
burns steadily as shown by the meters, note the 
amount of amperage and voltage required for the 
lamp. 

Watts = Volts X amperes 

Calculate the number of watts of power required 
to operate the lamp. 

Results. — 

Current strength = 
Electromotive force = 
Electrical power = 

Discussion. — Just as water power depends upon 
water pressure and the quantity of water flowing per 
second, so electrical power depends upon electrical 
pressure and the quantity of electricity flowing per 



68 



Laboratory Manual in Physics 



second. The unit of electrical pressure is the volt, 
and the unit of quantity of electricity per second is 
the ampere. Electrical power, therefore, is equal to 
amperes multiplied by volts. The unit of electrical 
power is the watt. One ampere flowing under a 
pressure of one volt is equivalent to one watt. 

Consult a reference for an explanation of the con- 
struction and operation of the arc lamp. 

EXPERIMENT No. 37 



Question. — What is the efficiency of the electric 
motor in the laboratory? That is, what per cent of 
the electrical power put into the motor is gotten out of 
it in the form of mechanical power? 

Apparatus. — Motor; ammeter; voltmeter; two 
spring balances; brake belt; speed indicator; watch. 




Directions. — To obtain the number of watts 
electrical power put into the motor, connect the 



Electricity and Magnetism 69 

ammeter in series and the voltmeter in parallel with 
the motor as shown in Diagram No. 1. 

To obtain the mechanical power gotten out of the 
motor make use of the brake shown in Diagram No. 2, 
consisting of two spring balances B and C and a 
friction belt passing under the pulley P. Raise the 
rod supporting the balances until the pointers of B 
and C stand about midway on the scales. If the 
motor rotates in the direction indicated by the arrow 
there will evidently be more pull on balance C than 
on balance B. The difference between the readings 
of the balances gives the pounds pull on the face of 
the pulley. 

One student should read the ammeter and volt- 
meter; a second student, the balances; and a third, the 
speed indicator and watch. 

Before starting the motor, disconnect the belt from 
the balance B. Throw in the switch and move the 
lever of the starting resistance slowly to the off 
position. When the motor has come to speed replace 
the belt on the balance B. Note the number of 
revolutions made in one minute, and during the entire 
time observe the balances and the ammeter and volt- 
meter in order to get their average readings. 

Calculate the input of electrical power. Amperes 
multiplied by volts equal watts. To what is this 
equivalent in horse-power? 

(1 horse-power = 746 watts) 

Calculate the output of mechanical power. The 
number of foot-pounds of work done during the one 
minute is the measure of the output. The pounds 



70 Laboratory Manual in Physics 

pull on the friction belt is evidently the difference 
between the readings of the two balances. During 
one revolution of the motor this pounds pull acts 
through a distance equal to the circumference of the 
pulley. With a pair of calipers measure the diameter 
of the pulley and calculate the circumference in feet. 
The foot-pounds of work done by the motor during 
one revolution is therefore equal to the pounds pull 
multiplied by the circumference of the pulley. The 
foot-pounds of work per minute done by the motor 
is evidently equal to the work done during one revo- 
lution multiplied by the number of revolutions made 
in one minute. To what is this equivalent in horse- 
power? (1 horse-power = 33,000 foot-pounds per 
minute). 

Calculate the efficiency of the motor. You have 
already learned that the efficiency of a machine is 
equal to the ratio of the output to the input. 
Results. — 
Input: 
Volts 

Amperes = 

Watts 

Horse-power = 
Output: 

Reading of balance D = 

Reading of balance C = 

Pounds pull = 

Diameter of pulley = 

Circumference of pulley = 

Foot-pounds during one revolution = 



Electricity and Magnetism 71 

Number of revolutions per minute = 
Foot-pounds per minute = 

Horse-power = 

rrr • Output 

Efficiency = z = 

Input 

Discussion. — How does the efficiency of an electric 
motor compare with that of a water motor? (Exper- 
iment No. 14.) 

To what are the losses in an electric motor due? 
Is there any friction due to the atmosphere? If you 
place a thermometer on the field or armature windings 
before and after a run you will find that there is a rise 
in temperature. What is the cause of this? 

Can we run a 4-horse-power motor with a 4-horse- 
power dynamo? Why? 

Problem. — An electric motor delivers 10 horse- 
power. If it has an efficiency of 90 per cent how 
many amperes are required to run it on a 110-volt 
circuit? 

EXPERIMENT No. 38 

Question. — How much heat is radiated per second 
by a 110-volt 16-candlepower lamp? Is there any 
definite relation between the amount of heat produced 
and the electrical power required to run the lamp? 

Apparatus. — Calorimeter; 16-candlepower lamp; 
voltmeter; ammeter; Fahrenheit thermometer. 

Directions. — Connect the ammeter in series and the 
voltmeter in parallel with the lamp. (Caution. — 
Show the connections to the instructor before turning 



72 Laboratory Manual in Physics 

on the current.) Place in the calorimeter one pound 
of water. The water should be as cold as can be 
drawn from the faucet. Take the temperature of the 
water, leaving the thermometer in the calorimeter. 
Immediately place the lamp in the water and note the 
time. The lamp should be held so that the brass 
base is just above the surface of the water. Let run 
for ten or fifteen minutes. The meters should have 
uniform readings throughout the experiment. Remove 
the lamp, quickly stir the water with the thermometer, 
and take the final temperature. 

Bearing in mind that one B. T. U. is the amount of 
heat required to raise the temperature of one pound of 
water 1° F., calculate the number of B. T. U. given 
out by the lamp during the time of the experiment. 
How many B. T. U. per second? Knowing the 
number of watts (amperes X volts) required to produce 
this amount of heat per second, you can calculate the 
number of watts required to produce 1 B. T. U. per 
second. 

Results. — Weight of water = 

Rise in temperature = 

Number of seconds = 

Total number of B. T. U. = 

B. T. U. per second = 

Watts (amperes X volts) = 

Watts for 1 B. T. U. per second = 
Problems. — One B. T. U. per second is equivalent 
to what horse-power? 

How many watts of power are required to run an 
electric heater that furnishes 820 B. T. U. an hour? 



Sound 73 

EXPERIMENT No. 39 

Question. — Why do different sized organ pipes or 
tuning-forks emit different pitched tones? 

Apparatus. — Rotator; speed indicator; siren disk; 
tuning-fork; blow-pipe; watch. 

Directions. — Place on the shaft of the rotator the 
siren disk. Using the blow-pipe, force a continuous 
blast of air through one of the rows of holes of the 
disk. Cause the rotator to revolve at such a speed 
that a sound is produced of the same pitch as the 
tuning-fork. By means of the speed indicator note 
the number of revolutions of the disk in one minute. 
Calculate the number of revolutions per second. 
Count the number of holes in the row used and multi- 
ply by the number of revolutions per second. This 
will give the number of holes passing by the blow- 
pipe in one second, or the number of puffs of air per 
second. Since the disk and tuning-fork produce the 
same tone, the number of puffs per second equals the 
vibration frequency of the tuning-fork. 

Results. — 

Number of revolutions per minute = 
Number of holes in row = 

Number of puffs per second = 

Discussion. — When the tuning-fork vibrates, it 
periodically condenses the air in front of the prong 
once during each vibration, causing so many conden- 
sations per second. Similarly, when the air is blown 
through the row of holes of the disk, these holes being 
equal distances apart, the air is cut up at regular 



74 Laboratory Manual in Physics 



\ £ ■■-- ]^ intervals into just so many puffs or 



condensations per second. 

Explain why different sized tuning- 
forks, organ pipes, or other musical in- 
struments produce tones of different 




pitch. 



EXPERIMENT No. 40 




Question. — How fast does sound travel 
through the air? 

Apparatus. — Glass tube fitted with 
stop-cock; tuning-fork of know T n pitch; 
centigrade thermometer. 

Directions. — Close the stop-cock and 
nearly fill the glass tube with water. 
Strike the tuning-fork with a rubber or 
cork mallet and hold in the position 
shown in the diagram as near to the 
opening of the tube as possible. Open 
the stop-cock a little and let the water 
flow until a point B is found where 
the sound of the tuning-fork is best 
resonated by the air column. Mark 
this point B with a thread or rubber 
band. Now let the water flow again 
until another point C is found where 
the tuning-fork is resonated as be- 
fore. The points B and C should 
be well fixed by a second or third 
trial if necessary. Measure the 



7 



Sound 75 

length BC in centimeters. This length BC is one- 
half of the length of a sound wave produced in the air 
by this particular tuning-fork. 

Explanation. — When the tuning-fork moves from 
a to b a condensation of air is produced. When the 
water stands at B, this condensation moves down the 
tube to B and back to A in time to join the prong in 
its upward movement from b to a, thereby increasing 
the sound. That is, while the tuning-fork is making 
one-half of a vibration (aft), one-half of a wave- 
length is formed (A to B and back to A). Therefore 
AB is one-fourth of a wave-length. Again, when the 
water stands at C the prong makes three half-vibra- 
tions beginning at a, while the condensation runs 
down the tube and back. Therefore AC is three- 
fourths of a wave-length or BC is one-half a 
wave-length. 2BC = 1 wave-length. The number 
stamped on the tuning-fork represents the number of 
vibrations or wave-lengths made by it in one second. 
Multiplying, you have the distance sound travels in 
air in one second. 

The colder the air the slower sound travels. There 
is a variation of 60 centimeters for each degree cen- 
tigrade. How fast would sound travel at 0° C? 
Take the temperature of the air in the tube, and 
calculate the velocity at 0° C. 

Results.— Length of air column BC = 

Length of sound wave = 

Number of vibrations of fork = 

Velocity of sound at C. = 

Velocity of sound at 0° ( \ = 



76 Laboratory Manual in Physics 

Discussion. — If you had used a different pitched 
tuning-fork the velocity of sound would have been 
found to be the same. If you had used a tuning-fork 
having twice the vibration frequency, what length 
would the air column have to be in order to 
resonate it? 

Give examples of musical instruments that make use 
of resonating air chambers. 



EXPERIMENT No. 41 



Question. — What effect has varying the length of 
the string upon the pitch of the tone produced? 

What effect has tension? 

Apparatus. — Sonometer; set of tuning-forks; two 
steel wires of same diameter. 

Directions. — To show the effect of length, tune one 
of the wires on the sonometer to the C-fork (256 
vibrations per second). Measure the length of the 
string. Now shorten the string to one-half its 
original length by means of the movable bridge. 
Find a tuning-fork which makes the same number of 
vibrations per second. Record this number and the 
length of the string. 

To show the effect of tension, tune one of the wires 
to the C-fork, the other to the fork an octave higher. 
Record the vibration frequencies and tensions of the 
wires. 



Sound 



77 



Results. — 



Effect of Length 


Effect of Tension 


Length 


No. of Vibrations 


Tension 


No. of Vibrations 







Discussion. — Do you find that the pitch of a wire is 
proportional to its length? Which wires in a piano give 
the notes of highest pitch? Of what use are the frets 
on a banjo? 

Extract the square-roots of the tension in the above 
results and note whether the vibration frequency of 
a wire is proportioned to the square-root of its length. 
How is a piano tuned? 

Why was it necessary to have the wires of the same 
diameter in this experiment? 



78 



Laboratory Manual in Physics 



EXPERIMENT No. 42 

Question. — Of what use is the pupil of the eye? 
Apparatus. — Dark room; optical bench; gas jet or 
candle; screen; piece of card-board. 




\ 



N 



U'lumiMUimiMMug 



<^Vn 



"^ 



asrnanxsmmsrcamH nttmg 




Directions. — Arrange the apparatus as shown in the 
diagram, with the gas jet, turned flatwise, at one end 
and the screen at the other. Make a hole in a piece 
of card-board with the point of the pencil and mount 
it between the flame and the screen. Observe the 
image of the flame on the screen. Account for its 
being inverted. Move the card-board back and forth 
and account for the varying size of the image. Make 
a diagram of rays of light leaving the upper and 
lower parts of the flame passing through the aperture 
and striking against the screen. 

Gradually enlarge the hole in the card-board until 
it is an inch or so in diameter and note the effect on 
the image. Explain the cause of this effect. 



Light 



79 



Discussion. — Explain the use of the pupil of the eye. 

If the lens of the eye were removed, as is sometimes 
done, without injuring the other parts, would you be 
able to see anything? 

When the oculist introduces atropine into the eye 
to enlarge the pupil, objects are then seen indistinctly. 
Why? Have a fellow student look toward the light, 
then away from it, and note the change in the size of 
the pupil. Why does the eye make this accommoda- 
tion? 

When you are taking a photograph in the bright 
sunshine why should you use a small aperture of 
the camera? 

EXPERIMENT No. 43 

Question, — Why is the vision of a far-sighted 
person corrected by the use of convex lenses? Test 
lenses of different convexity for their focal length. 

Apparatus. — Dark room ; optical bench ; two lenses 
of different convexities ; concave lens ; screen ; gas jet. 




"<£" 



Directions. — Arrange the gas jet, lens, and screen on 
the optical bench as shown in the diagram. Adjust 




80 Laboratory Manual in Physics 

the flame and screen until positions are found equi- 
distant from the lens, and at the same time a distinct 
image is formed on the screen of the same size as the 
object. Measure the distance from the lens to the 
screen. Half this distance is the focal length of the 
lens. Test the other lens of different convexity in 
the same manner. 

Test a concave lens in the same way. Are the rays 
of light brought to a focus or do they diverge? 

Results. — Record the focal lengths of the lenses. 

Discussion. — What effect has a convex lens upon the 
rays of light? Is it the lens of greater convexity that 
has the greater converging power? 

The lens of the eye is a double convex lens. In a 
far-sighted person this lens does not converge the rays 
sufficiently to produce a clear image on the retina of 
the eye. Explain the defect of the lens, and why a 
convex lens is used to correct the vision. 

What is the defect of the eye of a near-sighted person 
and why does a concave lens correct it? 



Light 81 



EXPERIMENT No. 44 



Question. — How can the magnifying power of a 
telescope be determined? 

Apparatus. — Telescope ; optical bench or sunlight. 

Directions. — Place on the blackboard a horizontal 
scale in inches, making the division marks very clear. 
At a distance of ten or fifteen feet, place the telescope 
and carefully focus it upon the scale. Determine how 
many divisions of the scale as seen by one eye without 
the use of the telescope will just cover one division as 
seen through the telescope at the same time by the 
other. This will give the magnifying power. It may 
take some time to accustom the eyes to use the 
instrument in this way and to adjust it so that one 
scale will be seen superposed on the other. 

Remove the lenses from the telescope, being careful 
not to injure them in any way, and find their focal 
lengths by means of the optical bench as explained in 
the preceding experiment; or, the focal length may 
be found by the sunlight. Focus the parallel rays 
of the sun on a screen, being careful that the lens is 
perpendicular to the rays. The distance from the 
lens to the screen is the focal length. It has been 
shown that the magnifying power is equal to the focal 
length of the object-glass divided by the focal length 
of the eye-piece. Find the magnifying power in this 
way and compare the result with that obtained in 
the first part of the experiment. 



82 



Laboratory Manual in Physics 



Results. — 

Magnifying power by scale comparison = 
Focal length of object-glass (F) = 

Focal length of eye-piece (/) = 

Magnifying power = F -£- / = 

Discussion. — Consult your text book or a reference 

for a description of the astronomical telescope. 

Construct a diagram tracing the rays of light through 

the lenses to the eye. 



EXPERIMENT No. 45 

Question. — What is the candlepower of an ordinary 
gas jet? Of a Welsbach burner? 

Apparatus.— Dark room ; optical bench ; photo- 
meter ; standard candle ; gas jet ; Welsbach burner. 




© 




■^T 



Directions. — Place the standard candle at one end 
of the optical bench, the gas jet turned flatwise at the 
other end, and the photometer between the two. The 
candle should be kept trimmed so that the flame will 
be as near 3 c. m. long as possible. Note the oiled 
translucent spot in the center of the photometer 
screen. By looking into the mirrors placed at an 
angle of 45° to the screen, the observer can determine 



Light 83 

whether one side of the screen is illuminated more 
than the other. Move the screen until it is equally 
illuminated on both sides; that is, when the distinc- 
tion between the oiled spot and the rest of the screen 
almost wholly disappears. Measure the distances 
from the screen to the candle and from the screen to 
the gas jet. 

The gas jet must have more than one candlepower 
since it produces at a greater distance than the candle 
the same illumination. It has been shown that 
when two lights illuminate an object equally, their 
c:i;idlepowers are proportional to the squares of their 
distances from the object. In other words, if the gas 
jet were twice as far away as the candle it would have 
4-candlepower ; 3 times as far, 9-candlepower ; 4 times 
as far, 16-candlepower; etc. Therefore, to find the 
candle-power of the gas jet, divide its distance from 
the screen by the distance of the candle from the 
screen and square the quotient. 

In like manner find the candlepower of the Wels- 
bach burner. 

Results. — 

Distance of candle (d) = 

Distance of gas-jet (D) = 

/D 2 \ 

Candlepower of gas-jet = I — j = 

Distance of Welsbach burner = 

Candlepower of Welsbach burner = 

Discussion. — Why does a Welsbach burner give 

more light than an ordinary gas-jet? Does it use as 

much gas? Which will give more illumination, a 



84 Laboratory Manual in Physics 

candle at a distance of one foot or a 16-candlepower 
lamp at a distance of four feet? 



EXPERIMENT No. 46 

Question. — What is the efficiency of a carbon 
filament lamp? Of a Tungsten lamp? 

Apparatus. — Optical bench; photometer ; standard 
candle ; carbon filament and tungsten lamps ; ammeter ; 
voltmeter. 

Directions. — The efficiency of an electric lamp is 
measured by the number of watts per candlepower 
required to run the lamp; the less the number of 
watts per candlepower the higher its efficiency. Let 
us see which has a higher efficiency; the carbon 
filament lamp, or the tungsten lamp. 

Find the candlepower of each lamp according to 
directions given in Experiment No. 45. Also find 
the number of watts required for the lamp by the 
method given in Experiment No. 36. Calculate the 
number of watts per candlepower. 
Results. — 

I. Carbon filament lamp 

Distance of lamp from screen = 

Distance of candle from screen = 

Candle-power of lamp = 

Amperes = 

Volts 

Watts = 

Watts per candlepower = 



Light 85 

II. Tungsten lamp 
(Same data) 

Discussion. — Which has a higher efficiency, the 
carbon filament or the tungsten? 

The consumer is charged for electric lighting so 
much per kilowatt-hour. A kilowatt equals 1000 
watts. A kilowatt-hour is the electrical work done 
in 1 hour at the rate of 1 kilowatt. Suppose you wish 
to light a house with twenty 32-candlepower lamps 
and burn all of them on an average of 4 hours a day. 
If electricity costs 10 cents per kilowatt-hour what will 
be the difference in cost per month (30 days) by using 
tungsten lamps instead of carbon filament lamps? 



APPENDIX I 
EXPERIMENT A 

Question. — Does the use of dye in coloring thread 
black affect its strength? 

Test the breaking-strength of black and white 
cotton thread of the same size and make. 

Apparatus. — Tensile machine; white and black 
thread, of same number, as coarse as can be obtained, 
and of same make. 




Directions. — Arrange the wedges of the instrument 
as shown in the diagram with one supported on the 
table and the other resting in the slot. Pass one end 
of the thread to be tested through the hole in the crank- 
shaft, and turn the crank so that the thread will wind 
itself several times around the shaft. Pass the 
other end of the thread once around the horizontal 
post of the sliding frame and then clamp under the 
binding screw. With the left hand, keep a slight 

86 



Miscellaneous Experiments 87 

pressure on the upper wedge so that it will fill the slot 
as the sliding frame moves forward. By turning 
the crank, increase the tension on the thread until 
it breaks. 

Test each kind of thread five or six times in order 
to get its average breaking-strength. 

Results. — 

Average breaking-strength of white thread = 
Average breaking-strength of black thread = 

Discussion. — Does the use of dye affect the strength 
of the thread? What kind of material is used for 
making the strongest fishing lines? Of what are tent 
ropes made? 

Piano wires are made of what material? Why? 
Why do the lead cables used by telephone companies 
have to be suspended every foot or so from an iron 
cable? Of what material are suspension bridges 
constructed? 



EXPERIMENT B 

Question. — Why will an auger bit stand a certain 
amount of twisting without changing its shape? Is 
there any definite relation between the twisting force 
and the amount of distortion? 

Apparatus. — Torsion frame with grooved wheel 
marked in degrees and vernier attachment; scale 
pan and weights; iron or steel rod. 



88 Laboratory Manual in Physics 

Directions. — Thoroughly clamp the rod in the 
frame. See that the zero of the vernier is just oppo- 
site the zero on the wheel when no weight hangs from 
the wheel. Place weights in the pan until the total 
weight, including the weight of the pan, equals 500 
grams, and note the amount of torsion in degrees. 
Read to tenths of degrees by means of the vernier. 
If the zero of the vernier does not come exactly 
opposite a mark on the wheel, look along the vernier 
until you find two marks that come exactly in a line. 
The number of the line on the vernier, counting from 
zero, will give the number of tenths of degrees. 
Remove the weight and note whether the scale returns 
to zero. In like manner, take readings for 1000, and 
2000 grams. 

Results. — 



Twisting Force 


500 gm. 


1000 gm. 2000 gm. 


Distortion 




. 



Discussion. — What relation exists between the 
amount of distortion and the force applied? Is the 
rod permanently distorted? What name is given to 
this property of matter which causes the rod to return 
to its original shape? Is the frame of a bicycle in use 
subject to twisting forces? May the twisting force 
sometimes be great enough to permanently distort 
the frame? Is there then an elastic limit to steel? 
Name some substances that have a lower elastic 
limit than steel. 



Miscellaneous Experiments 
EXPERIMENT C 



89 



Question. — Why does a pendulum clock always 
have some means for adjusting the length of the 
pendulum? 

Is there any definite relation between the length of 
a pendulum and the time of its vibration? 

Apparatus. — Pendulum support; thread; iron ball; 
watch. 

Directions. — Fasten to the support a pendulum one 
hundred centimeters long. The length of the pendu- 
lum should be measured carefully from the point of 
support to the center of the bob. By amplitude of 
vibration is meant the distance the bob is drawn to 
one side from the vertical. Using a small amplitude, 
count the number of single vibrations made by the 
pendulum during one minute. Repeat the operation, 
shortening the pendulum to seventy-five centimeters, 
and again to fifty centimeters. 

Results. — 



Length of Pendulum 


Number of Vibrations 
in One Minute 


Time of One 
Vibration 





















Discussion. — Is the time of vibration of a pendulum 
proportional to its length; that is, if we double the 
length, is the time of vibration twice as long? Sup- 



90 Laboratory Manual in Physics 

pose you extract the square-root of the length of the 
pendulum in each of the above cases. Do you find 
that the time of vibration of a pendulum is propor- 
tional to the square-root of its length? 

What force causes the pendulum to return each 
time to the middle point of its swing? Is this a con- 
stant force? Would a pendulum clock be possible 
if the force were not constant? Why? 

If you move a pendulum clock into a very warm 
room will it gain or lose time? Why? 

Will a pendulum clock gain or lose time if you take 
it to the top of a high mountain? Why? To the 
sea level? To the equator? To the north pole? 



EXPERIMENT D 

Question. — A man falling off a tower 200 feet high 
will strike the earth with what velocity? 

Apparatus. — Acceleration apparatus using a tuning- 
fork for the falling body. 

Directions. — Note the mechanism at the top of the 
apparatus for holding the tuning-fork. Place the 
tuning-fork in position, and hang from its projecting 
shank a plumb bob, adjusting the leveling screws in 
the base of the instrument so that the fork will fall 
vertically. By turning the lever, the tuning-fork 
is released and at the same time is set in vibration. 
As the fork descends it traces a wavy line on the 
smoked glass. Stamped on the fork is the number 
of vibrations it makes per second. The distance the 



Miscellaneous Experiments 



91 



fork falls during one vibration is 
measured by the length of the wave 
made during that period. Note that 
the wave-lengths get longer, the 
further the fork descends, that is, the 
greater the distance passed over dur- 
ing one vibration of the fork. Let us 
now find the velocity with w^hich the 
fork is moving at certain points dur- 
ing its fall. Through the wavy line 
draw a line, 10 centimeters from the 
starting point and letter it a. On 
each side of a mark off two wave- 
lengths and letter these points b and c, 
respectively. Measure the distance 
be with a pair of dividers and rule. 
The fork moved from b to c while it 
was making 4 vibrations. Therefore 
the velocity of the fork at a in centi- 
meters per second is equal to the 
distance be, divided by the time of 4 
vibrations. In like manner find the 
velocity of the fork at 40 centimeters 
from the starting point. 

Count the number of wave-lengths 
from the starting point to the 10 
centimeter mark, and calculate how 
long it took for the fork to fall this 
distance. How much did the 
fork change its velocity during 
this time? How much would 




92 Laboratory Manual in Physics 

the fork change its velocity during 1 second? In like 
manner calculate how long it took for the fork to fall 
from the 10 centimeter mark to the 40 centimeter 
mark, and how much it changed its velocity during 
this time; consequently how much it would change 
its velocity during 1 second. 

From the results obtained we conclude that the 
rate of change of velocity {i.e., the acceleration) of a 
falling body is uniform. You have found the accel- 
eration in centimeters per second. What is this 
equal to in feet per second ? 
Results. — 

Velocity of fork at 10-centimeter mark = 
Time required to fall 10 centimeters = 

Acceleration during this time = 

Acceleration for 1 second = 

Velocity of fork at 40-centimeter mark = 
Time required to fall from 10-centimeter 

to 40-centimeter mark = 

Acceleration during this time = 

Acceleration for 1 second = 

Discussion. — From results obtained you will note 
that the velocity of the fork is equal to the acceleration 
multiplied by the time it has been falling, or 
v = a t (1) 

Also, that the velocity is equal to twice the distance 
divided by the time, or 

" = T < 2 > 

Multiplying equation (1) by equation (2) we have 
V 2 = 2 a s, or V = V2^~s 



Miscellaneous Experiments 



93 



Using this formula, you can work the problem 
given at the beginning of the experiment. 

Give other illustrations of accelerated motion 
besides that of a falling body. 

When water is poured from a pitcher, why is the 
stream thinner at the bottom? 

Does a bullet fired vertically upward return to the 
earth with the same velocity with which it left the 
gun? Why? 

A paper bag full of water dropped from an upper 
story is dangerous to the passerby, while the water 
is not dangerous if poured from the bag. Why? 

EXPERIMENT E 



Question. — What is the resistance of a 16-candle- 
power carbon filament lamp when cold? 

Apparatus. — Wheatstone's bridge; galvanometer; 
resistance box ; electric lamp ; one or two cells. 



g— fl R 



oo 
o o 
o o 
oo 
oo 



0=0=6 



AE 



x^ 



Directions. — Connect the apparatus as shown in 
the diagram. X and Y are wires leading to the 



94 Laboratory Manual in Physics 

battery; AA f , a high resistance wire one meter long, 
stretched on a meter-stick ; G, a galvanometer ; £, the 
lamp to be tested; R, a resistance box; P, a sliding 
piece, for making contact with the wire, and electri- 
cally connected to S f , a broad bar having practically 
no resistance. 

Trace the direction the current takes when P is 
raised. It enters X (say) and is divided into two 
parts at A, one of which goes through E and R, and 
the other from A to A' where the two branches join 
and return to the battery through Y. 

The principle of the Wheatstone bridge is this; 
since the current divides at A and is united again at 
A f , the fall of potential along the two branches is the 
same. If P is in such a position that a current passes 
through the galvanometer, the fall of potential from 
A to 5 is not the same as the fall of potential from 
A to S f . But when there is no flow through the gal- 
vanometer, the fall of potential from i to 5 is the 
same as from A to S'. Or, in other words, the fall of 
potential in E is equal to the fall of potential in K, 
and the fall of potential in R is equal to the fall of 
potential in L. Since this is true, 

E _K 
R~ L 
Knowing the values of R, K, and L, found by the 
experiment, the value of E, the resistance of the lamp, 
can be determined. 

Introduce a resistance of 200 ohms in R. Move P 
along the wire A A' until a point is found where no 
current passes through the galvanometer. Measure 



Miscellaneous Experiments 95 

the lengths of the divisions of the wire, K and L. 
Compute the resistance of the lamp. 
Results. — 

Length of wire, K = 
Length of wire, L = 
Resistance, R = 

Resistance of lamp = 
Discussion. — Why should the wire A A 1 be of the 
same diameter throughout? 

Examine a 32-candlepower carbon filament lamp. 
Is the filament of a different length or diameter than 
that of the 16-candlepower? Why is this difference 
made? Examine a tungsten, or tantalum lamp, and 
give the reason for using a filament of such a length 
and diameter. 



EXPERIMENT F 

Question. — Upon what does the voltage of a dyna- 
mo depend? 

Apparatus. — Dynamo belted to motor; speed 
regulator for motor ; rheostat ; voltmeter. 

Directions. — Start the motor and bring it to its 
highest speed by gradually moving the arm of the 
speed regulator to the off position. Close the circuit 
which excites the field of the dynamo. Connect 
the voltmeter to the brushes of the dynamo and test 
its voltage. Now change the speed of the dynamo 
armature by changing the speed of the motor and 
note the effect on the voltage. 



96 Laboratory Manual in Physics 

The armature rotates in a magnetic field produced 
by the current flowing through the field windings. 
What effect will changing the strength of the field 
have upon the voltage set up in the armature? Place 
a rheostat in series with the field coils so as to lessen 
the amount of current going to the field. Note the 
effect on the voltage by introducing more or less 
resistance in the rheostat. 

Discussion. — The voltage set up in the armature is 
caused by the coils of wire on the armature cutting 
the lines of magnetic force passing between the north 
and south poles of the field magnet. The greater 
the number of lines of force cut per second, the higher 
the voltage. Therefore, if we were to increase the 
number of turns of wire on the armature, what effect 
would be produced on the voltage? 

Explain the effect of changing the speed of the 
armature. 

Explain the effect of changing the strength of the 
magnetic field. How would you change the field 
windings so as to increase the magnetic strength of 
the field? 

If you wished to construct a dynamo having a very 
high voltage would ygtu wind the armature with 
large or small wire? Why? 



Miscellaneous Experiments 
EXPERIMENT G 



97 



Question. — Why is the image in a plane mirror 
reversed ? 

Apparatus. — Rectangular mirror attached to block; 
cardboard; pin; rule. 




Directions. — Write your name on a piece of paper, 
hold it in front of the mirror and note the image 
formed. Is it reversed? Let us locate the image 
formed by the mirror of some simple object such as a 
triangle and see the reason for its being reversed. 

Draw a straight line through the middle of the card- 
board and place on it the reflecting or back surface of 
the mirror. In front of the mirror, and to one side as 
shown in the diagram, draw a triangle, ABC. The 
image of the triangle can be located by locating the 
images of its vertices, A, B, and C. Stick a pin 
vertically in the card-board at A. To the left of the 
triangle lay a rule on the card-board and sight along 
its edge to the image of the pin. Draw a line to 



98 Laboratory Manual in Physics 

indicate this direction. The image of A must lie 
somewhere in the line produced. Move the rule to 
one side and again locate by a line the direction in 
which the image is seen. The intersection of these 
two lines produced must be the location of the image 
of A. Letter this point of intersection A f . In like 
manner locate B' and C . Connect A' , B\ and C . 

Discussion. — Does the location of A 'B'C explain 
why the image formed by a plane mirror is reversed ? 
Is a photograph of yourself the same as your image in 
a mirror? Has the image a fixed position no matter 
from what position you view it in front of the mirror? 
Connect A and A' \ B and B' '; C and C . How does 
the distance of the image from the mirror compare 
with the distance of the object? When you approach 
a full-length mirror, what does your image do? 

EXPERIMENT H 

Question. — When looking at a pond of water at an 
angle, why does its depth appear less than it really is? 

Apparatus. — Semi-circular glass vessel, the plane 
side being opaque with a vertical slit in the center 
through which light may pass, the half-circle being 
transparent and graduated in degrees; candle; com- 
pass. 

Directions. — Fill the vessel one-third full of water 
and place the lighted candle in the position shown in 
the diagram. The incident beam of light CO will pass 
through the slit 0. The part of the beam above the 
water will not be refracted and will pass in a straight 
line to A. The part striking the water will be 



Miscellaneous Experiments 



99 




refracted and will go to B. Take the readings of A and 
B in degrees, counting from X, the zero of the scale. 

With compass, rule, and sharp pencil, lay off on a 
page of your notebook an accurate reproduction of 
the half-circle and the lines CO, OA, and OB. Draw 
the line XY perpendicular to the plane side of the 
vessel at 0. The angle CO Y is known as the angle of 
incidence. The angle BOX is known as the angle 
of refraction. The angle AOB is known as the 
angle of deviation. By reading A to get the measure- 
ment of angle A OX we get the measurement of angle 
COY. Why? 

Make another trial with the candle nearer to F, and 
still another with the candle at Y. 

Results. — 



Angle of Incidence 


1st Trial 


2nd Trial 


3rd Trial 


Angle of Refraction 








Angle of Deviation 









100 Laboratory Manual in Physics 

Discussion. — When light strikes the surface of water 
at an angle is it refracted? In what direction is the 
light wave bent, toward, or away from a line perpen- 
dicular to the surface? Which has a greater density, 
air or water? Do you think light moves more slowly 
in water than in air? Does this give you a reason for 
the fact that the light wave is bent the way it is when 
it enters water on a slant? 

When light passes from water into air which way is 
it bent, toward or away from the normal? Make a 
diagram showing why a pond viewed slantwise seems 
to have less depth than it really has. Why do we 
see the sun before it is actually "up?" What is the 
cause of the twilight after sunset? Why does a 
"burning glass" bring light to a focus? 

Why is a diamond such a brilliant stone? 



APPENDIX II 



TABLE I 
Densities in Grams per Cubic Centimeters 



SOLIDS 

Aluminum 2 . 56- 2 . 80 

Amber 1.06- 1.11 



Basswood . 

Birch 

Brass 

Cedar. . . . 



... .32- .59 
... .51- .71 
. .. 8.20- 8.60 
... .49- .57 

Copper 8.80-8.95 

Cork 18- .24 

Ebony 1.11- 1.33 

Spruce 48- .70 

Gold 19.26-19.34 

Hickory 60- .93 

Ice..... 88- .92 

Iron 7.03- 7.90 

Lead 11.36-11.40 

Limestone 2.46- 2.86 

Mahogany 56- .85 

Maple 62- .75 

Oak 60- .90 

Pine 46- .59 

Silver 10.42-10.57 



LIQUIDS 

Alcohol (95 %)..... .820 

Ether .736 

Mercury 13.596 

Naphtha, wood 810-. 848 

Naphtha, petroleum . 665 

Oil, linseed .940 

Oil, olive .915 

Oil, turpentine .870 

Water... 1.000 

Water, sea 1 .026 



GASES AT 0° C. AND 
76 CM. PRESSURE 

Air 001293 

Carbon dioxide 001977 

Hydrogen 000896 

Nitrogen 001256 

Oxygen 001430 



Air. 



TABLE II 
Specific Heats 

. . 237 Iron. . 



Aluminum 218 

Brass 086 

Copper 093 

Hydrogen 3.409 

Ice 505 



113 

Lead 031 

Mercury 033 

Silver 056 

Water 1.000 



102 Laboratory Manual in Physics 



TABLE III 

Diameter of Wire, Brown and Sharpe'a U. S. 
Standard Gauge 



Gauge 
Number 


Diameter 
Inches 


Diameter 
Millimeters 


Gauge 
Number 


Diameter 
Inches 


Diameter 
Millimeters 


0000 


.4600 


11.684 


17 


.0453 


1.1495 


000 


.4096 


10.405 


18 


.0403 


1.0237 


00 


.3648 


9.266 


19 


.0354 


0.9116 





.3249 


8.251 


20 


.0320 


0.8168 


1 


.2893 


7.348 


21 


.0285 


0. 7249 


2 


.2576 


6.543 


22 


.0253 


0.6438 


3 


.2294 


5.827 


23 


.0226 


0.5733 


4 


.2043 


5. 189 


24 


.0201 


0.5106 


5 


.1819 


4.621 


25 


.0179 


0.4545 


6 


.1620 


4.115 


26 


.0159 


0. 4049 


7 


.1443 


3.665 


27 


.0142 


0. 3606 


8 


.1285 


3.264 


28 


.0126 


0.3211 


9 


.1144 


2.906 


29 


.0113 


0. 2859 


10 


.1014 


2.588 


30 


.0100 


0. 2546 


11 


.0907 


2.305 


31 


.0089 


0.2268 


12 


.0808 


2.053 


32 


.0079 


0.2019 


13 


.0720 


1.828 


33 


.0071 


0.1798 


14 


.0641 


1.628 


34 


.0063 


0. 1601 


15 


.0571 


1.450 


35 


.0056 


0. 1426 


16 


.0508 


1.2908 


36 


.0050 


0.1270 



Tables 103 



TABLE IV 
Useful Data 



x = 3.1416 

Area of circle = x R 2 . 

1 in. = 2.54 cm. 

1 meter = 39.37 in. 

1 oz. avoirdupois = 28.35 gm. 

1 kgm. = 2.2 lb. 

1 liter = 2.11 pints. 

1 cu. cm. water weighs 1 gm. 

1 liter water weighs 1 kgm., or 2.2 lb. 

1 gal. = 231 cu. in. 

1 gal. water weighs 8.35 lb. 

1 cu. ft. water weighs 62.5 lb. 

1 cu. ft. air at 0° C. weighs .080728 lb. 

1 H. P. = 33,000 ft. lb. per min. 

1 H. P. = 746 watts. 

1 B. T. U. = 252 gram calories. 

1 B. T. U. = 778 foot-pounds. 

1 B. T. U. per second = 1055 watts. 



SEP 16 1912 



LIBRARY OF CONGRESS 





003 752 907 2 
































































































































































